By Min Zeng 

U.S. government bonds strengthened Friday, capping the biggest weekly rally in price in four months.

Investors piled into the world's most liquid bond market for safety this week, sparked by fresh worries over the flagging economic recovery in the euro zone and financial health of a major bank in Portugal.

An additional boost for Treasury bonds came from the Federal Reserve, which continued to signal patience before shifting into raising interest rates. That indication came from the minutes of its June policy meeting released Wednesday.

"The percolating stress in Europe helped fuel this week's rally in bonds, " said Sean Simko, head of fixed-income management at SEI Investments, which has $209 billion in assets under management. "There is the growing view that a Fed rate hike may be further off than initially thought."

In late afternoon trade, the benchmark 10-year Treasury note rose by 3/32 in price, yielding 2.520%, according to Tradeweb. Yields on bonds fall when prices rise.

The yield fell by about 0.12 percentage point for the week, the most on a weekly basis since March. It has tumbled from 3% at the start of the year.

This year through Thursday, Treasury bonds have handed investors a total return of 2.63%, nearly eliminating the loss of 2.75% for the whole year of 2013, according to data from Barclays PLC. Total return include bond price appreciation and interest payments.

"The bond market has continued to frustrate those betting on higher yields," said Mark Lindbloom, portfolio manager at Western Asset Management Co., which has about $469 billion in assets under management. He said U.S. bonds' yields are low, but "they don't look that bad" compared with their counterparts in Germany and Japan, which lured buyers seeking relative value in a low-yield world.

Friday, the 10-year German government bond yielded 1.2% and the 10-year Japanese government bond yielded 0.53%.

Kevin Giddis, head of fixed income at Raymond James, said the 10-year Treasury yield could drop to 2.4%, which is this year's low and was set on May 29, or lower if "there is a spread in the risks of the [economic] recovery in Europe," or if the U.S. growth fails to live up to market expectations, pushing the Fed to hold interest rates low for longer than many expect.

Investors will zero in on Fed Chairwoman Janet Yellen's semiannual testimony before lawmakers on the economy and rate-policy outlook next week.

Ms. Yellen "is likely to maintain her dovish posture, further signaling that policy tightening remains well beyond the end of bond buying," said Christopher Sullivan, who oversees $2.3 billion as chief investment officer at the United Nations Federal Credit Union.

U.S. big banks still expect Treasury bond yields to rise in the second half of the year.

Strategists at Goldman Sachs Group Inc., J.P. Morgan Chase & Co. and Morgan Stanley expect the 10-year note's yield to rise to 3% by the end of the year to reflect the U.S. economy gaining momentum while inflation pressure continues to tick higher.

Corrections & Amplifications

Yields on bonds fall when prices rise. An earlier version of this article said bond yields fall when their yields rise.

Write to Min Zeng at min.zeng@wsj.com